We study the existence of particular traveling wave solutions of a nonlinear parabolic degenerate diffusion equation with a shear flow. Under some assumptions we prove that such solutions exist at least for propagation speeds cε]C*,+∞[, where C*>0 is explicitly computed but may not be optimal. We also prove that a free boundary hypersurface separates a region where u=0 and a region where u>0, and that this free boundary can be globally parametrized as a Lipschitz continuous graph under some additional non-degeneracy hypothesis; we investigate solutions which are, in the region u>0, planar and linear at infinity in the propagation direction, with slope equal to the propagation speed.
|Original language||English (US)|
|Number of pages||31|
|Journal||Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire|
|State||Published - 2013|
All Science Journal Classification (ASJC) codes
- Mathematical Physics
- Applied Mathematics